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Scattering of solitons for the Schrödinger equation coupled to a particle |
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| Authors: | A Komech E Kopylova |
| Institution: | (1) Faculty of Mathematics of Vienna University, Nordbergstrasse 15, 1090 Vienna, Austria;(2) M. V. Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Miusskaya pl. 4, Moscow, 125047, Russia;(3) Present address: Department of Mechanics, Mathematics of Moscow State University, Russia |
| Abstract: | We establish soliton-like asymptotics for finite energy solutions to the Schrödinger equation coupled to a nonrelativistic classical particle. Any solution with initial state close to the solitary manifold converges to a sum of a travelling wave and an outgoing free wave. The convergence holds in global energy norm. The proof uses spectral theory and the symplectic projection onto the solitary manifold in the Hilbert phase space. |
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